1. Show that the following pairs are logically equivalent: a. P^ (Q V R); (P^ Q)V (P ^ R) b. P v (Q ^ R ); (PVQ)^ (P V R) c. P + Q; (P → Q) ^ (Q →P) d. P → Q; ~Q →~P
1. Show that the following pairs are logically equivalent: a. P^ (Q V R); (P^ Q)V (P ^ R) b. P v (Q ^ R ); (PVQ)^ (P V R) c. P + Q; (P → Q) ^ (Q →P) d. P → Q; ~Q →~P
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![1. Show that the following pairs are logically equivalent:
a. P^ (Q V R); (P^Q) V (P ^ R)
b. P v (Q ^ R); (PVQ)^ (P V R)
c. P + Q; (P → Q) ^ ( Q → P)
d. P → Q; ~Q →~P
'
2. Prove the following logical implications:
a. (P ^ Q) -→ Q
b. (Р^@) —Р
c. [(P → Q) ^P] → Q
d. [(P → Q) ^ (P VR)]→(Q VR)
3. Show that the following pairs are not logically equivalent:
PA -Q
-P → - Q
-P V - Q
a. ~ (P ^ Q);
b. - (P → Q);
c. ~ (P V Q);](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fd7bbcf-0993-40bd-8850-4df6892ba12c%2Fb3c17869-06d8-4e38-a87d-e2d8e8ae3332%2F0ap9of_processed.png&w=3840&q=75)
Transcribed Image Text:1. Show that the following pairs are logically equivalent:
a. P^ (Q V R); (P^Q) V (P ^ R)
b. P v (Q ^ R); (PVQ)^ (P V R)
c. P + Q; (P → Q) ^ ( Q → P)
d. P → Q; ~Q →~P
'
2. Prove the following logical implications:
a. (P ^ Q) -→ Q
b. (Р^@) —Р
c. [(P → Q) ^P] → Q
d. [(P → Q) ^ (P VR)]→(Q VR)
3. Show that the following pairs are not logically equivalent:
PA -Q
-P → - Q
-P V - Q
a. ~ (P ^ Q);
b. - (P → Q);
c. ~ (P V Q);
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